$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting

• URL: http://arxiv.org/abs/2505.23017v3
• Date: Sat, 26 Jul 2025 14:24:12 GMT
• Title: $K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting
• Authors: Xingjian Wu, Xiangfei Qiu, Hongfan Gao, Jilin Hu, Bin Yang, Chenjuan Guo,
• Abstract summary: Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation.<n>We introduce $K2$VAE, an efficient VAE-based generative model that transforms nonlinear time series into a linear dynamical system.<n>$K2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.
• Score: 11.83736650205371
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). As the forecast horizon extends, the inherent nonlinear dynamics have a significant adverse effect on prediction accuracy, and make generative models inefficient by increasing the cost of each iteration. To overcome these limitations, we introduce $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.

Related papers

• Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update [60.414548453838506]
  We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function.<n>GLBs are widely applicable to real-world scenarios, but their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency.<n>We propose a jointly efficient algorithm that attains a nearly optimal regret bound with $mathcalO(1)$ time and space complexities per round.
  arXiv  Detail & Related papers  (2025-07-16T02:24:21Z)
• Does Scaling Law Apply in Time Series Forecasting? [2.127584662240465]
  We propose Alinear, an ultra-lightweight forecasting model that achieves competitive performance using only k-level parameters.<n>Experiments on seven benchmark datasets demonstrate that Alinear consistently outperforms large-scale models.<n>This work challenges the prevailing belief that larger models are inherently better and suggests a paradigm shift toward more efficient time series modeling.
  arXiv  Detail & Related papers  (2025-05-15T11:04:39Z)
• Timer-XL: Long-Context Transformers for Unified Time Series Forecasting [67.83502953961505]
  We present Timer-XL, a causal Transformer for unified time series forecasting.<n>Based on large-scale pre-training, Timer-XL achieves state-of-the-art zero-shot performance.
  arXiv  Detail & Related papers  (2024-10-07T07:27:39Z)
• TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting [49.6208017412376]
  TimeBridge is a novel framework designed to bridge the gap between non-stationarity and dependency modeling.<n>TimeBridge consistently achieves state-of-the-art performance in both short-term and long-term forecasting.
  arXiv  Detail & Related papers  (2024-10-06T10:41:03Z)
• MixLinear: Extreme Low Resource Multivariate Time Series Forecasting with 0.1K Parameters [6.733646592789575]
  Long-term Time Series Forecasting (LTSF) involves predicting long-term values by analyzing a large amount of historical time-series data to identify patterns and trends. Transformer-based models offer high forecasting accuracy, but they are often too compute-intensive to be deployed on devices with hardware constraints. We propose MixLinear, an ultra-lightweight time series forecasting model specifically designed for resource-constrained devices.
  arXiv  Detail & Related papers  (2024-10-02T23:04:57Z)
• Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction [54.21695754082441]
  Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility. Current solutions to multi-step stock price prediction are mostly designed for single-step, classification-based predictions. We combine a deep hierarchical variational-autoencoder (VAE) and diffusion probabilistic techniques to do seq2seq stock prediction. Our model is shown to outperform state-of-the-art solutions in terms of its prediction accuracy and variance.
  arXiv  Detail & Related papers  (2023-08-18T16:21:15Z)
• OFTER: An Online Pipeline for Time Series Forecasting [3.9962751777898955]
  OFTER is a time series forecasting pipeline tailored for mid-sized multivariate time series. It is specifically designed for online tasks, has an interpretable output, and is able to outperform several state-of-the art baselines. The computational efficacy of the algorithm, its online nature, and its ability to operate in low signal-to-noise regimes render OFTER an ideal approach for financial time series problems.
  arXiv  Detail & Related papers  (2023-04-08T00:18:03Z)
• EgPDE-Net: Building Continuous Neural Networks for Time Series Prediction with Exogenous Variables [22.145726318053526]
  Inter-series correlation and time dependence among variables are rarely considered in the present continuous methods. We propose a continuous-time model for arbitrary-step prediction to learn an unknown PDE system.
  arXiv  Detail & Related papers  (2022-08-03T08:34:31Z)
• Low-Rank Temporal Attention-Augmented Bilinear Network for financial time-series forecasting [93.73198973454944]
  Deep learning models have led to significant performance improvements in many problems coming from different domains, including prediction problems of financial time-series data. The Temporal Attention-Augmented Bilinear network was recently proposed as an efficient and high-performing model for Limit Order Book time-series forecasting. In this paper, we propose a low-rank tensor approximation of the model to further reduce the number of trainable parameters and increase its speed.
  arXiv  Detail & Related papers  (2021-07-05T10:15:23Z)
• On projection methods for functional time series forecasting [0.0]
  Two nonparametric methods are presented for forecasting functional time series (FTS) We address both one-step-ahead forecasting and dynamic updating. The methods are applied to simulated data, daily electricity demand, and NOx emissions.
  arXiv  Detail & Related papers  (2021-05-10T14:24:38Z)
• Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting [98.57851612518758]
  Probabilistic time series forecasting involves estimating the distribution of future based on its history. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks. We show in experiments that our model produces accurate and sharp probabilistic forecasts.
  arXiv  Detail & Related papers  (2021-01-31T06:49:33Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.